The unfavorable effects of recirculation in differential gear trains and continuously variable transmission were also reported by Pennestrì et al. At the very least, the allowed recirculation should not exceed a specified limit. Therefore, recirculation must be detected. In some cases, it can produce several times more useless power consumption inside the trains than the input. This portion of power does not produce a useful output. Recirculation generates circulating power inside the PGTs.
However, an undesired pattern of power flow, recirculation, in these trains is believed to be one of the leading causes of lower efficiency compared with simple gear trains. Therefore, efficiency often determines the final choice. Generally, these candidate configurations satisfy the motion design objectives. When designing such trains, the designer usually faces multiple candidate configurations during the conceptual design phase. Most automatic transmissions for passenger cars use parallel-connected planetary gear trains. Our results provide the underlying insights to understanding recirculation from the structural connection viewpoint, thereby contributing to the conceptual design phase where the task is to select the kinematic structure and the gear size is unknown. Thus, the recirculation of parallel-connected ring-sun-type PGTs can be predicted without calculations. A geometric model representing the structure and kinematics was developed to visualize the power flow. This shows that the structure, specifically whether the links are central gears or carriers, and the connections between them directly impact the recirculation of these PGTs. Two necessary and sufficient conditions, torque and structure, were proven for multi-stage and two-stage PGTs without recirculation, respectively. This study employs a generic model utilizing the mechanical balance principle and reveals the fundamental laws of the previously unexplained connection for parallel-connected ring-sun-type PGTs. However, it exhibits an unexplained connection with the structure, making it challenging to identify without tedious computation through tooth and speed ratios, thus complicating the design process. Recirculation is expected to be identified for its possibility to dramatically decrease the efficiency of planetary gear trains (PGTs).
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